Hidden Markov Models

pHMM too!

Markov Chain, Markov Model

• Markov Chain: describes a meaningful process that can be in any one of a number of states at any given time,

Markov Chain: Jeff plays guitar.

Markov Model: noun verb noun

Hidden Markov Model

...probabilistic model of a group of Markov Chains,

Hidden Markov Model: (noun) (verb) (adjective) (noun) (adverb)

Markov Chain(2): Jeff plays flamenco guitar.

Markov Chain(3): Jeff plays flamenco guitar poorly.

Markov Chain(1): Jeff plays guitar.

Markov Model: noun verb noun

Profile Hidden Markov Model

• A Hidden Markov Model built to describe a certain set of Markov Chains, that is used to identify additional, related chains...

Hidden Markov Model: p(Sentence) = p(Words in sentence)|(n)(v)(a)(n)(a)

x p(Word order)(n)(v)(a)(n)(a)

GC Rich vs. Normal

NNNNNNNNNRRRRNNNNNNNNNNNNNNNNNRRRRRRRNNNN

TTACTTGACGCCAGAAATGTATATTTGGTAACCCGACGCTAA

60% AT, 40%GC

Are the red regions really GC-rich (R)?

Training

A T G C

Normal (N) 0.3 0.2 0.2 0.2

GC-Rich (R) 0.1 0.4 0.4 0.4

Based on real data, the relative frequencies observed for base identification given genomic location (state probablilties)....

Based on real data, the probability of “entering”, or leaving a GC-rich or normal state…

N - N (0.9) N - R (0.1)C - C (0.8) C - R (0.2)

HMM p(ACGC)

N

A 0.3

T 0.3

G 0.2

C 0.2

N

A 0.3

T 0.3

G 0.2

C 0.2

N

A 0.3

T 0.3

G 0.2

C 0.2

N

A 0.3

T 0.3

G 0.2

C 0.2

0.9 0.9 0.9

R

A 0.1

T 0.1

G 0.4

C 0.4

0.1 R

A 0.1

T 0.1

G 0.4

C 0.4

0.1 R

A 0.1

T 0.1

G 0.4

C 0.4

0.1

0.8 0.8

0.2 0.2

p(ACGC|NNNN)p(NNNN) = 0.00175 p(ACGC|NRRR)p(NRRR) = 0.00123

HMM p(ACGCC)

N

A 0.3

T 0.3

G 0.2

C 0.2

N

A 0.3

T 0.3

G 0.2

C 0.2

N

A 0.3

T 0.3

G 0.2

C 0.2

N

A 0.3

T 0.3

G 0.2

C 0.2

0.9 0.9 0.9

R

A 0.1

T 0.1

G 0.4

C 0.4

0.1 R

A 0.1

T 0.1

G 0.4

C 0.4

0.1 R

A 0.1

T 0.1

G 0.4

C 0.4

0.1

0.8 0.8

0.2 0.2

p(ACGCC|NNNNN)p(NNNNN) = 0.000315 p(ACGC|NRRRR)p(NRRRR) = 0.0004

Figure 1

Figure 2

Figure 3

HMM-Others